This can be written as the Ward-identity [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]},
\(\boxed{{\beta , out} Q^{out}_S(f){\alpha , in} - {\beta , out} Q^{in}_S(f){\alpha , in} = \bigg ( \sum _{i\in \alpha } \omega _i f(x_i) - \sum _{i\in \beta } \omega _i f(x_i) \bigg ) {\beta , out}{\alpha , in}}\) 
